Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints which introduce curvature into parameter space and discuss the appropriate mathematical tools for treating curvature effects. Channel capacity, a term from communication theory, is suggested as a useful figure of merit for estimating the information content of spectra in the presence of noise. The tools introduced here are applied to the case of a model nitroxide system as a concrete example, but we stress that the methods described here are of general utility.